Completing the DBQTM: Inflation from a Third Warped Throat

Abstract We complete the Dual-Brane Quantum Tunneling Model (DBQTM) by introducing a third Klebanov--Strassler throat as the inflationary sector. In the companion papers~\cite{DBQTM-Paper1,DBQTM-Paper2}, two warped throats on the same Calabi--Yau manifold were shown to generate the cosmological constant (Throat~1: $K_1=203$, $M_1=17$, $kd_1 \approx 375$) and dark matter (Throat~2: $K_2=39$, $M_2=35$, $kd_2 \approx 35$, $m_\mathrm{DM} \approx 133$~GeV). A shallow third throat with $(K_3, M_3) = (3, 27)$ and $kd_3 \approx 3.5$ provides a GUT-scale IR sector at $\Lambda_{\mathrm{IR},3} \approx 6.5 \times 10^{15}$~GeV. The K"ahler modulus of this throat, stabilized via the KKLT mechanism with $SU(27)$ gaugino condensation, naturally produces a Starobinsky-like $\alpha$-attractor inflationary potential ($\alpha = 1$), predicting $n_s = 0.964$ and $r = 0.004$, both consistent with Planck and testable by LiteBIRD and CMB-S4. The scalaron decay produces a reheating temperature $T_\mathrm{RH} \approx 2.5 \times 10^9$~GeV, precisely in the range required for gravitational freeze-in production of the dark matter candidate in Throat~2. All three cosmological sectors --- dark energy, dark matter, and inflation --- are thus determined by seven discrete flux integers $(K_1, M_1, K_2, M_2, K_3, M_3, g_s)$ and one continuous parameter ($k/M_\mathrm{Pl}$), with verifiable cross-predictions linking the inflationary observables to the dark matter abundance.